{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PHydro-cover-small.png\">\n",
    "*This is the Jupyter notebook version of the [Python in Hydrology](http://www.greenteapress.com/pythonhydro/pythonhydro.html) by Sat Kumar Tomer.*\n",
    "*Source code is available at [code.google.com](https://code.google.com/archive/p/python-in-hydrology/source).*\n",
    "\n",
    "*The book is available under the [GNU Free Documentation License](http://www.gnu.org/copyleft/fdl.html). If you have comments, corrections or suggestions, please send email to satkumartomer@gmail.com.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Empirical Distributions](05.01-Empirical-Distributions.ipynb) | [Contents](Index.ipynb) | [The t-Test](05.03-The-t-Test.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.2 理论分布\n",
    "\n",
    "理论分布是基于数学公式而不是经验观测。有各种不同类型的理论分布，常用于水文学的中的有:正态分布、均匀分布、、指数分布、卡方分布、柯西分布。分布的参数称为位置、尺度和形状参数。位置参数是\n",
    "在不影响其他属性的情况下更改pdf位置的那个参数。形状参数是在不易宁乡其他属性情况下改变分布形状的参数。拉伸或缩小分布的参数称为尺度参数。首先我们将生成正态分布随机变量。需要输入的是位置和尺度参数，在正态分布情况下是平均值和标准偏差。我们也可以使用`np.random.randn`来生成正态分布的随机变量，但是`scipy.stats`提供了许多其他的工具(方法)。所以我们要使用`scipy.stats`库。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as st\n",
    "\n",
    "# 生成正态分布随机变量的例子\n",
    "rv1 = st.norm(loc=0,scale=5)\n",
    "rv2 = st.norm(loc=0,scale=3)\n",
    "rv3 = st.norm(loc=0,scale=7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在这些变量的例子可以用于评估任何值的PDF。在下面的例子，我将出于绘制图形的目的从-50到50计算pdf。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-50,50,1000)\n",
    "y1 = rv1.pdf(x)\n",
    "y2 = rv2.pdf(x)\n",
    "y3 = rv3.pdf(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在，我们已经估计了PDF，它可以被绘制。在x轴我们将保留变量，并在y轴保留PDF。我们还为`plot`函数提供了额外的参数`lw`，它代表了线宽，并且用来控制图形的宽度。如图5.7显示了具有不同尺度参数的三个正态分布随机变量的PDF。该图说明了尺度参数对PDF的影响。在较小尺度参数的情况下，随着尺度参数的增加，越来越多的pdf集中在中心，其传播范围也在不断扩大。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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0Fnq0e20or0lSFkCMiaWezkJvY5MJTR+Q8AAiInNFZIOIbBaR26JcTxeRxf7rH4vIaP/5VBFZKCJrRWS9iNye6LIbc0ixaMICa8IyfUJCA4iIuIFHgbOBycB8EZkcke1qoFJVxwMPAff5z18EpKvqFOBY4B/agosxSSMWneiR91oTlklSia6BzAI2q+oWVW0BFgHnReQ5D1joTz8PzBERARTIFpEUIBNoAWoSU2xjOilsFnr0AOLx+ti8t5ZdVY0dP8cmE5o+ICXBnzccKA05LgNmd5RHVT0iUg0U4gST84ByIAv4saraLCuTXMJmobcPIK+uKeeeV9axp6YZgBklA7nvgqlMGJwbntGasEwfkOgaiEQ5FzlLqqM8swAvMAwYA/yTiIxt9wEi14rIChFZsW/fvp6W15iuOUgfyB8+2s4NT68MBA+AlTuquOjxD9m4pzb8OTYb3fQBiQ4gZcDIkOMRwK6O8vibq/KAA8D3gNdVtVVV9wIfADMjP0BVn1DVmao6s7i4OA6vYMxBdLCQ4sodlfxsybrA8YCMFFLdzu9KVQ2tXLNwBQ0tnuC9tiuh6QMSHUCWAxNEZIyIpAGXAEsi8iwBFvjTFwJvq6oCO4AzxJENHA98maByG3NoPl/UhRS9PuXW59fg9TmV7akj8njv1jP483UnkpPutCLvONDAL9/YGHKvNWGZ5JfQAKKqHuBGYBmwHnhWVdeJyD0icq4/25NAoYhsBn4CtA31fRTIAT7HCUS/U9U1iSy/MQfVVAXqddLpAyAlHYAXVpaxaW8dANlpbh793gzyMlOZOmIg//Kt4CDE33+4nZ1tHes2Csv0AYnuREdVlwJLI87dHZJuwhmyG3lfXbTzxiSNKB3orV4fD7+1KXD62lPHMbIgK3B84bEjWLS8lE+3V9Li9fHoO5v59/OnQGY+iAvUB03V4G0Fd2rCXsWYzrCZ6MbESpQhvH9dvydQqyjITuPqU8aE3SIi/OQbEwPHL67cSU1Tq7OKb6YtZ2KSmwUQY2IlygisP360I3Dqe7NKAn0eoU4cV8iRQ5xhvI2tXl74tMy5kGVzQUxyswBiTKxEzELftr+e9zc7P/hdAvNnl0S9TUS49PhRgeM/fbwDVQ0fiWU1EJOELIAYEysRTVh/WR0coX76EYMYPjCzw1vPP2Y4WWluADbtreOL8pqIjnSrgZjkc8gAIiIn+ofNGmMOJrQTPbuIV9eWBw7PnT7soLfmpKfwjcmDA8evrCm3FXlN0utMDeQ94Ki2AxFxici7IjIhfsUypg8K6afY683hy93O7PL0FBdzJg3u6K6AeVODQeaVNbtQ60Q3Sa4zASRyaREBTgZyo+Q15vAV0sz08e7gt81pRxRH7TyPdOrEInIznHylBxop9+REfbYxycL6QIyJlZBawjtl3kD6m1OGdur29BQ3c44cFDhecyAk6NgoLJOELIAYEysh/RQr9jkd4iku4YyQoHAop4fk/WhPyAVrwjJJqLMz0S8QkbaFC104q+NeJCLHR+RTVX0sZqUzpi8J+SF/QJ0W3mNH5ZOb0fkZ5F+bWIxLwKfwyV4XpLV/tjHJorMB5JYo526Nck4BCyDm8NPaCK31AHhIoQ5nyO6pE7u2IvTArDRmlOSzYnslFb4BwQvWhGWS0CGbsFTV1YUvdyIKbUzSCfkBf4ABtI09+VoXAwgEm7EqQ8epNFQ4q/0ak0SsD8SYWAhpYqrwOaOninLSmDx0QEd3dKgt6LSQGqjJoF5oru55OY2JoU6vxuvfl/wbOPtwtA1q3wN8CLzl37PDmMNTyDDbCn//x6kTinG5om2weXCThw4gLzOV6sZWKny55Lj8S7zXVzir9BqTJDoVQETkGGAxMA5nW9n9OHX0Qv8zNorIJaq6Kl4FNSaphcxCd5qw4JSJRR3lPiiXS5g9poA3vthDJbmMYq//M/YD43taUmNipjNLmQzG2QCqEfgmkKOqw1R1KM5kwnOAFmCZiHR+vKIx/UloH4i/BnL82MKOch/SCeOceys0pAnMRmKZJNOZPpCbcILHKaq6TFVb2i6oarOqvgac6s9zY3yKaUySawgNIAMoKchiaF7HiyceSlsAaQtGgI3EMkmnMwHkTODXqlrTUQZVrcIZvjs3VgUzpk8JnQNCLrPGFBwk86FNHJRLQXYaB8JGYlkAMcmlMwFkPLCyE/k+xRpozeEqoglr1uieBRCXSzh+bAEHwpqwDnR8gzG9oDMBJA/ozPjBWqDrYxaN6Qc0pAZSGYMaCDh9KGE1EGvCMkmms6vxdnaIbtfHLBrTD7RU7w2kNauIUYVZPX7msaPywzrR1ZqwTJLp7DyQZSLiicWzRGQu8CvADfxWVe+NuJ4O/B44FqgALlbVbf5rU4HHcWo6PuA4VW3q5DsYEzehP9xHl4zCmTbVM0cOGUBjSl7guLV2X2BpLGOSQWd+6P88Vh8mIm7gUZwJiWXAchFZoqpfhGS7GqhU1fEicglwH3CxiKQAfwQuV9XVIlIItMaqbMZ0m7eVjFanldenwtHjR8fksW6XMHTYSNjtHHtqLICY5HLIAKKqPxeRTJw5IKNx/jm/pap7DnpjdLOAzaq6BUBEFgHnAaEB5DzgZ/7088Aj/lnwZwJrVHW1v1w2KN4kBW2oCLTdVpLDsWO6vv5VR8aOGhUIICnN1olukktnJhKOBdYBzwIPAH8ANojImd34vOFAachxmf9c1Dyq6sHpwC8EJgIqIstEZKWI/HM3Pt+YmNu3Z1cgXcUAJg6O3WadU8aOoMW/RmmarwlaGmL2bGN6qjOd6Pfj9DecCmTh7I/+GU5fRFdFaxiO7KDvKE8Kzla6l/r/f76IzGn3ASLXisgKEVmxb9++bhTRmK7Zsm1bIN2cXoi7G+tfdWR6SX5gaRSAhqq9B8ltTGJ1JoCcAPxUVT9Q1SZVXQ/8A1AiIp3bqzOoDBgZcjwC2NVRHn+/Rx5wwH/+b6q6X1UbgKXAjMgPUNUnVHWmqs4sLo5dU4IxHdm1K1ipdud0b/2rjuRlplLvHhg43rRta0yfb0xPdCaADAW2RJz7CqemMKSLn7ccmCAiY0QkDbgEWBKRZwmwwJ++EHjbv9LvMmCqiGT5A8vXCO87MaZXVO4L/g6UlX/wbwlVZUv1Fv6+8+98VP4R+xsPPTRXs4JzSrbv2NH9ghoTY50dxhuTpdpV1SMiN+IEAzfwlKquE5F7gBWqugR4EviDiGzGqXlc4r+3UkR+iROEFFiqqq/GolzGdFeLx0dT9Z7Ar2KFg4ZFzdfoaWTRl4v40/o/sachfPzJ9OLpXHX0VZw+8vSow3/TBwyCOie9u3xnTMtvTE/0dB7IXyPPq+pBV+RV1aU4zU+h5+4OSTcBF3Vw7x9xhvIakxTWl9eQ76sOBJBoNZB1+9dx63u3sr1me9RnrNq3ih++80POGHkG95x0D3npeWHX84qGBhp6qyrK8fm0W/uMGBNrCZ0HYkx/89mOSoZIbfBEdngfyPs73+fH7/yYJm9wvmtuWi6TCibR5G3ii4ov8Pic38HeLn2bra9t5bGvP8bwnODgxNyCwYF0tqeKLfvrGT8oJ05vZEzndWoeSCIKYkxf9FlpFZdKyELVWcEA8m7Zu/zwnR8GAkR2ajY/mvEjvjPhO6S5nSmB+xv38+tVv+a5jc8BsLV6K9e+cS0Lz15IUabzLAkJSvnU8tmOSgsgJinYnujG9MBnO6ooJCSAZDsj/zZWbuSWv90SCB7DsoexeN5iLjnykkDwACjKLOLuE+7mgVMfINWVCsCO2h1c/9b1NHr8W9mGBKVCqeWz0qo4v5UxnWMBxJhu2l/XzI4DDRSG1kCyi6htqeUf3/5HGjzOpL9h2cNYePZCRg0Y1eGz5o6ZywNfewCXON+S6w+s595P7g08s02B1LBye2XsX8aYbrAAYkw3rdpRRQoeBkq9c0JckJnPvZ/cy846Z7RUdmo2j8x5hCHZhx7xPqdkDnfOvjNw/MKmF3hlyyuQFdwat4BaNu6ppa75UGubGhN/FkCM6abPSivJJ6QDPbOAt0rfYclXwalNPz/x50zIn9DpZ1408SLOGXtO4PjeT+6lwuUOHBdILT6FNWXWjGV6nwUQY7rpsx1VFIU0X9VmF/KLj34ROD5n7DmcNfqsLj1TRLjr+LsCo7Cqm6u5f91vaVvhJ1/qcOPlsx0WQEzvswBiTDd4fcrq0ioKQgLIY9kpHGhyVswdlDmIO2bf0a1nZ6dmc9fxdwWOl257jQ/ygs1Y+dTx2Q7rBzG9zwKIMd2weW8d9S3ewAisr1JTeCZkPsjNx93MgLTu7/B80vCTwpqyHszLpq3XI19q+WxHFc4KP8b0HgsgxnTDqlKnBtA2AuvBgvzAD/iZg2cyd/TcHn/GzTNvJivF2Rp3s1t5OSc78JkV9S3sOGBLu5veZQHEmG5Y5Z+LUSC1rExP5/2sTABc4uK2WbfFZEvboswivn/09wPHj+QPpEGEAn+tx/pBTG+zAGJMN7T98C6giv/KD65dNW/sPI4oOCJmn3PFUVcwKNNZXm5/ipunB+RS4G8qs34Q09ssgBjTRQ0tHjbucX6IV2Xt59PMDABSxMUPpv0gpp+VmZLJ9dOvDxwvzMslV5zgZTPSTW+zAGJMF60tq8anAMpfi4Id5+cPPYWRuSM7vK+7zh1/LsNSnLWvqtxudgx09gT5YlcNTa3emH+eMZ1lAcSYLmrr/3BnbWFTujMSKlWVa4+6Mi6fl+pK5ZohpwaOVxZUgLTg8Slrd1bH5TON6QwLIMZ0UVsASSv8W+DcebV1DCk+Km6f+e2RpzPE44zzqnP7SM3/GLB+ENO7LIAY00WrS6twpe8iJWcjAKLKlY1AambcPjM1ZzDXVAUnLablfwB4Wbnd+kFM77EAYkwX7K1pYld1E2mF7wbOfb2hkVGZRQe5Kwayijivrp58r9Pn4UqrIiX3c1buqLQJhabXWAAxpgs+K61CUg+QMmBN4NzVVTWQM/ggd8VAdhEZqlxcUxc4lVb4HntrmyivbjrIjcbEjwUQY7pgVWkVaQUfIOIDYHZjE0e1tEDOoPh+cGompGZzSU0tac4QMNyZZbgzt9qEQtNrLIAY0wUrS3eTmrcicHxltb9fIvfQ+330WFYhhT4f36qrD5xKLXyPldaRbnpJwgOIiMwVkQ0isllEbotyPV1EFvuvfywioyOul4hInYjcnKgyGwPOCrzrat5G3M0AlLiyObHR33wU7xoIQLazIu8VNcHO9JScL/m49Mv4f7YxUSQ0gIiIG3gUOBuYDMwXkckR2a4GKlV1PPAQcF/E9YeA1+JdVmMibd5biy/3g8DxpSlFwW+gePeBAOQOBWBsq4cTc51NqkSUr5rfpNljEwpN4iW6BjIL2KyqW1S1BVgEnBeR5zxgoT/9PDBH/CvTici3gS3AugSV15iAl778G+70vQC4yODclpDRTwkMIAAL8oLrbbkHrGDljt3x/3xjIiQ6gAwHSkOOy/znouZRVQ9QDRSKSDZwK/Dzg32AiFwrIitEZMW+fftiVnBj3tr5QiA9Ked0cmpD/n0lOIAc700hS5x+F3E3sXj9ko7uMiZuEh1Aoq1xHTmIvaM8PwceUtW6KNeDGVWfUNWZqjqzuLi4m8U0Jtyuul3sbv00cHzhhIuhbk8wQyICyIBgAHHV7ub4om8Fjj+qWGLzQUzCJTqAlAGhq82NAHZ1lEdEUoA84AAwG7hfRLYBPwLuEJEb411gYwCe/mIxiPMD2lM/njPHHgFN/uGz4oaswoPcHSMhNRBqy5k/6TuoLw2Aei1jxZ4VHdxoTHwkOoAsByaIyBgRSQMuASLr3kuABf70hcDb6jhFVUer6mjgYeDfVfWRRBXcHL6aPE08v+n5wHGR9wwGeA4EM2QXgysB30oRAeTYkmH4amcETv3v2j/FvwzGhEhoAPH3adwILAPWA8+q6joRuUdEzvVnexKnz2Mz8BOg3VBfYxLp9W2vU+9xhs76WgZy0rBToCak4jxgWGIKEtKERU05qS5hfPpZgVPv73qH3fXWmW4SJyXRH6iqS4GlEefuDkk3ARcd4hk/i0vhjImgqjy9/unAcWvlCcycUQQ1HwczJSqAZAyElAzwNEFrPTS5kgELAAAduElEQVTXcsLIo9i0bQwp2Vvx4eP5jc9z4zHWsmsSw2aiG3MQq/etZv2B9QCoL4WW6pkcOyo/ogYSOZAwTkTaNWMdUzKQ1soTA6ee2/gcLd6WxJTHHPYsgBhzEM98+Uwg7amZRmFGPqMLs3qnCSvys2rLOaYkH0/tZHytAwA40HSAN7a/kbjymMOaBRBjOrC/cX/YD+OWyhM5dlQ+IgI1O4MZE1UDgfA1t2rKGTwgg+EDc2itnB04vejLRYkrjzmsWQAxpgPPb3wej8/ZBdDbMApf03Cn+Qp6rwYS1oTllGF6yUBaq2ah6gacZrd1FbZYg4k/CyDGRNHqa+W5Dc8FjlsqTwBg5uheDiBhTVjOiKtjRg5Evbl4aqYELj2z/pnIO42JOQsgxkTx9o632dvorHvl8+TgqTmaNLeLo4fngdcT+OENhNcK4i2sCcsJYjP8taKWA8HO9Ne2vkZlky3zbuLLAogxUYR2njv9CylMGZFHeoob6veC+le/zSqC1IzEFSy0v8XfD3PUsAGkuV34mkbibRwBQIuvhRc2vRDtCcbEjAUQYyJsOLCBT/c4614JblqrnA7qmb3d/wGQF7ISUNUOANJT3EweNgCQQFMbwOINi/H6bJl3Ez8WQIyJsGhDcBRTZut01OMMkZ01psA5WV0WzJzIEVjgNGG5Up10QwW0OLsTHlMyEABPzVTSJReA8vpy/q/s/xJbPnNYsQBiTIjq5mpe3fJq4Lhi10wAXALHtQUQ/2/+AAwMXRs0AVxuyAsJWv5gNqPEXzvSVAZ4Tg5cDm2KMybWLIAYE+LlzS/T6GkEYFjmWDwNowE4engeAzL8v/mHBZBRCS4hEc1YzvY6bR3pALtKp+MS51v74/KP2VK1JaHFM4cPCyDG+PnUF9Z8Ncz1ddq2pzl+bMhy7VXbg+mBJQkqXYjQoOUvy/CBmYwqzAKgqTGPaQUnBbJYLcTEiwUQY/w+2PkBpbXOb/S5abnsKZ8UuHZCWAAJqYHk90INJLTZrDq4weeJ44JlHMycQHrJV0uoaznoPmzGdIsFEGP8/rQ+uJ/GN0efx/pdzYDT/xGYQKga0YTVCzWQKE1YACeOKwqkt5UNZVzeOAAaPA28/NXLCSueOXxYADEG2FS5iQ92fQCAIIxLP5O2HWKnDM8jt63/o34/tDY46fQ8yMyP8rQ4Cw1aIcHshJAayKrSKi6Y8N3A8aIvF+FTX0KKZw4fFkCMAX7/xe8D6Tklc9i0Mz1wfPy4JOr/gA6bsIpy0jlyiDOEt9WrDHadTE5qDgDbarbxbtm7CS2m6f8sgJjD3v7G/WFDdxcctYD3Nu0LHJ/QUQd6b/R/gDP3RJyFE6kth5aGwKXQWsin2+q5cOKFgePfff67hBXRHB4sgJjD3tPrn6bV1wrA1OKpFKcdwaa9TqdzeoorfARWZWgNpJcCiDs1vPZTuTWQDO0H+fvmCi6ddCkp4mw8unLvStbsW5OwYpr+zwKIOaw1tDbw7MZnA8cLJi/g3Y3B2sfssYVkpLqDN4T8sO61JiyAwnHBdMVXgeTssQW4Xc7Q4893VZOq+Xxz7DcD1/933f8mqoTmMGABxBzWlny1hOrmagCG5wxnTskc/rYhGEBOnVAUfsP+zcF00fhEFDG6gpAAciAYQAZkpHKsf1a6Kvzfhn0sOGpB4Ppb299iR03IKDJjesACiDlstfpaw34jv3zy5fhU+GDz/sC5044oDr+pYlMwXdiLAaSDGgjAaUcGy/z2hr1MzJ/IScOciYWKhg0YMKYnEh5ARGSuiGwQkc0icluU6+kisth//WMRGe0//w0R+VRE1vr/f0aiy276l1e3vMrOOmdJ9IHpAzl//Pl8tqOK2mZnF8LhAzMZV5wTvKGxCur9tRN3evh8jEQr6DiAnHHkoED63Y37aPX6uPLoKwPnXtr8Evsb92NMTyU0gIiIG3gUOBuYDMwXkckR2a4GKlV1PPAQcJ///H7gW6o6BVgA/CExpTb9kdfn5bdrfxs4vnzy5WSlZvHXL/cEzp06sdjZ/7xN6A/qwnHOwoa9pXBsMH0gPIAcMTiXYXnOHiW1TR5Wbq9k9pDZTC50vtWavc02IsvERKJrILOAzaq6RVVbgEXAeRF5zgMW+tPPA3NERFT1M1Vt24hhHZAhIukY0w2vb3ud7TXOiKrctFzmHzkfVeWNdcEAMifkN3kgeZqvAPJKwOWMrqJuDzTXBi6JCKeHlP3tDXsREX4w9QeBc89ueNZqIabHEh1AhgOlIcdl/nNR86iqB6gGCiPyXAB8pqrNkR8gIteKyAoRWbFv377Iy8bgUx+/WfObwPGlky4lNy2XTXvr2Lrf2V8jK83Nye060JMogLhTIH9M8Lhic9jl048IBpA3v9iDqnLayNOYVOCs79XkbbJaiOmxRAcQiXJOu5JHRI7Cadb6h2gfoKpPqOpMVZ1ZXFwcLYs5zL2x/Q2+qnaafbJSsrhs0mUALPs8uM/5aUcUhw/fhfAaSNGEuJfzkIqPCKb3fBF26eQJRWSlOeXfsq+eDXtqERGum3ZdII/VQkxPJTqAlAGhPY8jgF0d5RGRFCAPOOA/HgG8CFyhql9hTBe1+lp55LNHAsfzj5xPXnoeAMu+CAaQs44a0v7mfRuC6cIkCCCDjwqm94YHkIxUd1hn+tI15QDtaiFPff5U/Mtp+q1EB5DlwAQRGSMiacAlwJKIPEtwOskBLgTeVlUVkYHAq8DtqvpBwkps+pUXNr4Q1vdx1dFXAVBW2cDnO2sASHWH9yEA0NoU0oQlMGgSvW5QyPiTiAACcM6UoYH0q2vLUdV2tZBFXy4KjEQzpqsSGkD8fRo3AsuA9cCzqrpORO4RkXP92Z4ECkVkM/AToG2o743AeOAuEVnl/4r4LjemYw2tDTy2+rHA8TVTrgnUPv6yujxw/sRxRcHdB9vsWw/qddIFYyA9h14XWgPZ0z6AnHbEIDL9zXBf7atn4x5neZbTRp7G1OKpgFMj+9XKX8W/rKZfSvg8EFVdqqoTVXWcqv6b/9zdqrrEn25S1YtUdbyqzlLVLf7z/6qq2ao6PeRrb6LLb/quhV8spKKpAoDBWYP53pHfA0BVefGzskC+c6cNa3/z7rXB9JApcS1npxWMhRRnuC51u6HhQNjlzDQ3Z0wK/o716hqntVhEuHnmzYHzr219jbX71mJMV9lMdHNY2F2/O2zU0Q3TbyDD/8N3fXlt4LfzjFQXZx0dpf9j9+fB9OAkCSAud0RH+rp2WeaFNGP9eeVOfD5nPMoxg47hG6O+Ebj24IoHUY0cz2LMwVkAMYeFB5Y/QKOnEYAJ+RM4d9y5gWsvrQr2AZx11BBy0lPaP2BPSAAZcnTcytllg0KasXa3r0WcMWkQA7Oc5ridVY38/auKwLUfzfhR2Eq9S7cujW9ZTb9jAcT0ex/u+pA3tr8ROL5z9p24/bPIWzw+XlgZDCDnHxM5LQnw+cJrIMnShAUwfEYwvXNFu8vpKW6+PT34TotXBKdhlQwoYf6k+YHj+5ffH1hY0pjOsABi+rVmbzP//vG/B46/NfZbHDv42MDxsnW72V/nzEcdMiCDk8cXtXsGFZug7QdrVqGzoVOyGDEzmC5bHjXLd2cGR84vW7ebqoaWwPEN029gUJbTT3Kg6QAPr3w4PuU0/ZIFENOvPfrZo2yr2QZATmoOP5n5k7Drf/gouEHU/FklpLijfEvs+CiYHjkbJNpc114y+OhgR3rVDqhrP65k8rABTBnujDZr8fj4c0iNKzs1mztm3RE4fn7j86zcszK+ZTb9hgUQ02+t2rsqbLn2Hx/7Y4oygzWMDbtr+WSrM3IpxSVcMquD1XVLPw6mR86OR1G7z50KQ6cHj8vaN2MBYe/2uw+24vH6AsdnlJzBaSNPCxz/9IOfUt9aH/Oimv7HAojplxpaG7jrg7tQ/yo4xw89nosmXhSW5/F3g4sZnHnUYAYPyIj+sNAaSMnxMS9rj4U1Y30SNct3jhlBvr8zvayykWUhi0aKCHfMuoOcVGduS2ltKfcvvz9+5TX9hgUQ0++oKj//8OeBpqvs1GzuOfGesKXZSw808PKq4Co615wyNvIxjvr9weXS3Wnhv+0ni9Ba0dZ3o2bJTHNz2fHBPdyfeG9L2LDdoTlDuWN2sCnrhU0v8Ob2N2NfVtOvWAAx/c5zG58LG5J6x+w7GJozNCzPE+9uweufE3HC2EJm+LeBbWfL/wXTw2ZAage1lN405hQQ/7fyzpXtJhS2ufyEUaT5+3hWl1bxzobw/pJ5Y+dx9uizA8d3fXAXW6q3xKfMpl+wAGL6lVV7V3HfJ/cFjr8z4Tthcz4Atu2vZ9Hy4L7gN5x+kKXZN78VTI9L0k0wM/NheNvIMg0PeiEG5WbwvdklgeMHl20MTCwEpynrpyf8lOE5ziiz+tZ6fvj2D6lpqYlXyU0fZwHE9Bvba7Zz09s30eJzhqkekX8Et8+6vV2++17/klav84Nz5qh8Thofud2Mn88XHkDGfz3mZY6ZcXOC6a/+2mG2608fR0aq823/RXkNf1kTvhj2gLQBPHz6w2S4nZrWtppt3PK3W2j1tsa+zKbPswBi+oX9jfu57q3rqGquAqAgo4CHTnsosFxJm4+2VPBayL4fd54zKXzb2lA7VwT3QM8qhGHHxKXsMRFaO9rwOng9UbMNys3gqpOCG1H926vrqWkKDw5HFhzJL076ReD477v+zu3v347X541tmU2fZwHE9Hn7Gvbx/WXfp7TWmWWd4c7gv8/4b0YOCB+W29ji5bY/rwkcz5s6lGM66vsA+PzPwfSR54Arib9dRsyEHP8aXg37O2zGArj+tHEMynV2g95b28x/LtvQLs/cMXO5ftr1geNl25Zxz0f3WBAxYZL4O8KYQyuvK+eqZVextXorAG5xc9+p9wWWKw/1wLINbKtoACA3PYU7zznInh5eD6x7MXh89AUxLXfMudww5cLg8dpnO8yam5HKXfOCe4ks/HA7725sv/3zD6b9ILBiMTgjs25971ZrzjIBFkBMn7Vq7yrmvzo/sEFUiqRw/6n3c0ZJ+87u19aW89QHWwPHP503iaF5mR0/fMOrUOefK5E9CEadHNOyx8WUkHku61+BxqoOs86bOpTTjwhu+fyTZ1ext7YpLI+IcOusW8MGISzbtozr/nodVU0dP9scPiyAmD5HVXl2w7NcvezqwP4eKa4UHvzag5w5+sx2+deX13Dzc6sDx6cfURy2PlRUHz8eTB+7ANxRVuhNNkOnBXcpbK2HlQs7zCoi3H/hNIpynKas/XUtXLNwBfXN4X0nLnHxi5N+wfwjg4suflz+Md995bt8vv9zzOHNAojpU/Y17OOmt2/iFx/9IjDaamD6QH7zjd8wZ9Scdvk3763jst9+TH2L03ZfUpDFQxdP77jjHJzJeNv9uyaLG469KubvERcicHxwu1o+fBRaOl6SpDg3nYcvno7L/0expqya6/60ksaW8H4Ol7i4fdbt3Dj9xsC58vpyLn/tcn696te0eFswhycLIKZPaPG28OTaJ5n34jz+Vva3wPnxA8fz9DlPM3PIzHb3fLr9ABc//iEV9c4PuNyMFB6//FgGZqV1/EFeD7xxV/B4+nzIS6LVdw9lynch1z9psm4PvH/w1XVPnlDEL74d3N/k3Y37uOKpj8NW7AWnxvIP0/6BX53+K3JTcwHw+Dw8tvoxLvrLRfyt9G+2IdVhyAKISWr1rfUsXLeQs/98Ng+vfJgGT0Pg2mWTLuOZc55hZG54c5TPpzz5/lbm/+bjQPDISnPzv1fNYtLQAQf/wA8egvJVTtqdDl+7LabvE3epGXDGT4PH7/8SSqMv897m0tmj+PHXJwaOl2+r5Jz/ep8V29rPaD+j5AwWzVvEtOJpgXNbqrdw49s3cuXrV/LOjndspNZhRPrzbw0zZ87UFSuir05qkpfX52Xl3pW8suUV3tj2BnWtdWHXx+WN4/bZtzN7aPuVcT/aUsG9r33JqtJgJ29Bdhq/ueJYjh1VcPAPXvcSPHcl+BdgZM7dcMo/9fBteoHPC0/NDS6smDsMrnwFCscd9LbfvreFf311fdi5C48dwT+dObHdgAOvz8uiDYv4r5X/FRbUAYbnDOfb47/NmaPPZGxeB2uMmaQmIp+qavtqfWS+RAcQEZkL/ApwA79V1XsjrqcDvweOBSqAi1V1m//a7cDVgBf4R1VddrDPsgDSN3h8Hr6q+op1Fev4cNeHfFj+YdSd8Yoyi7hmyjV894jvkupKDZyvqGvmrfV7eOaT0rDAATBp6AAev+xYSgqzOi6A1wMfPAzv/Buof5nzkhNgwV+c5dL7osrt8Pgp0OT/c8weBOc/dsjZ9G9+sYebn1tNdWNwqG6KSzh7ylDOP2YYJ40vIj3FHbi2v3E/T6x5guc2PofH137y4ti8scwaMotZQ2cxtWgqg7IGHbz/ySSFpAwgIuIGNgLfAMqA5cB8Vf0iJM/1wFRV/YGIXAKcr6oXi8hk4BlgFjAMeAuYqKod1pctgCSHJk8TVc1VVDZVUtlcyd6GvZTWljpfNaVsrtpMk7epw/tHDxjNFUddwdxR86iqV8qrm9i6v451u2pYVVrF2p3VRP4zTnO7uPbUsfzjnAmkpURpqfW0wL4vYfOb8OlCqApuLEXBOLj6DciOsjthX7Ll/+DpS8C/FzwAo0+BaZfAmFMhb2TUzbF2VjXy8yXreOOLPe2uZae5OaYkn+kjB3Lk0FxG5mcxsiCLJt9+Fm9czJ83/fmg2+LmpecxYeAExg0cx5DsIc5X1hCKs4rJTcslNy037JcD0zuSNYCcAPxMVc/yH98OoKr/EZJnmT/PhyKSAuwGioHbQvOG5uvo87obQO783Xeo8VTS0Z+MRrkSek4BgbAfapH3BPKIggaP26519rMin9n+WDu4Hnk1+pWO/wyCKS/QKj5aRWkRpRWlVZyvJvHRIl3/N5bndTGtKZPZdVmMbErB54OWkE2QIn/sib9EIjA0L5PxxVlkpkYMvfW1OivVNuyH6p3OcaQRs+CSP0HOoC6XOSltex+eXeC8c6T0AZA7xFmmJWOgU9typ4IrFdwplNd6+HxXDXtrmjt8fNvfrIiQnuKCFNiUXcfazBq+TK+ltRt/9+nqIlPdpKuLFFykIKSokIKLVH/ahSBIoBPXOcL/5U8ruPz/Utqu9RbppU+fNvhkrjn3ni7f19kAkujB7cOB0pDjMiCyITuQR1U9IlINFPrPfxRxb1yGx3zm2UhpmlWzE2mwx8NRzS1Ma27mpIYmJra2tv+Wc0e7M4pa/1dXZObDyT+G42/oG3M+Omv0yXD9R/DmXbDmWQitsDfXOF8dGOr/6vRPCQVagSrnq1GEVelpLM/M4NOMdDakpVHfieVgmsVHs/gOmc8cWsa++LbAJPo7JdpP5chfUTrK05l7EZFrgWsBSkpK2t1gEi9FlXyvl4E+H/leH4VeLyM8Hka2ehjh8TCmpZUiXy/8wMgrgeEz4Iiz4ch5kJ6T+DIkQk4xnP8/cNrt8MXLTrPd7rXQWBnXj81U5YSmZk5ocmowCpSnuNmYmkZpagq7U9zsdrvZnZJCpdtFjctFrcuFz/pI+oxEB5AyIHTM5QhgVwd5yvxNWHnAgU7ei6o+ATwBThNWdwr5zYK51DW1DWGUQOgKrYaGpSV4NjSlIdXqtns09P6I54b+NzRcSsRzwXWI6yHnJLQsERVpkXZ5w58pkafDOkDb7nOLizRSSJXgV5qkkCZu0kkhXdID9zn/C/8BUQaUSnjZUlPcZKS6SE9xO1+pLrLSUkhxhZUm7DnR2vPD8rjckFngNNnkDob03Cj5+7H8UXDSPzpfqs5ui/X7oKECmqrA2wo+j///rc5oroMKfnu1epWmVi+N/i+PV/H5fHh9iteneHyKVxVVyFU4CmVyWzNpyHepT5UmPDRoC83qwYOPVrx48OFRbyDtw4fiNOeqv1FXUXz+BwavtZ3vv6NND2bS6BPj+vxEB5DlwAQRGQPsBC4BvheRZwmwAPgQuBB4W1VVRJYAT4vIL3E60ScA0TeA7qEbL3gwHo81JnmIODWTnOJD5+2EVP/XYRaSD3sJDSD+Po0bgWU4LdpPqeo6EbkHWKGqS4AngT+IyGacmscl/nvXicizwBeAB7jhYCOwjDHGxJdNJDTGGBOms6OwbCkTY4wx3WIBxBhjTLdYADHGGNMtFkCMMcZ0iwUQY4wx3dKvR2GJyD5g+yEzJp8iIMriRf2avfPhwd65bxilqoecJNSvA0hfJSIrOjOErj+xdz482Dv3L9aEZYwxplssgBhjjOkWCyDJ6YneLkAvsHc+PNg79yPWB2KMMaZbrAZijDGmWyyAJCERuVlEVESK/MciIv8lIptFZI2IzOjtMsaKiDwgIl/63+tFERkYcu12/ztvEJGzerOcsSQic/3vtFlEbuvt8sSDiIwUkXdEZL2IrBORH/rPF4jImyKyyf///N4ua6yJiFtEPhORV/zHY0TkY/87LxaRtN4uY6xYAEkyIjIS+AawI+T02Tj7n0zA2W3xsV4oWry8CRytqlOBjcDtACIyGWcp/6OAucCvRaSzm9omLf87PIrzdzoZmO9/1/7GA/yTqk4Cjgdu8L/nbcBfVXUC8Ff/cX/zQ2B9yPF9wEP+d64Eru6VUsWBBZDk8xDwz4Rv13se8Ht1fAQMFJGhvVK6GFPVN1TV4z/8CGenSXDeeZGqNqvqVmAzMKs3yhhjs4DNqrpFVVuARTjv2q+oarmqrvSna3F+oA7HedeF/mwLgW/3TgnjQ0RGAOcAv/UfC3AG8Lw/S796ZwsgSUREzgV2qurqiEvDgdKQ4zL/uf7m+8Br/nR/fef++l4dEpHRwDHAx8BgVS0HJ8gAg3qvZHHxMM4vgD7/cSFQFfJLUr/6+070lraHPRF5CxgS5dKdwB3AmdFui3KuzwyfO9g7q+rL/jx34jR7/Knttij5+8w7H0R/fa+oRCQH+DPwI1Wtkaj71vcPIjIP2Kuqn4rIaW2no2TtN3/fFkASTFW/Hu28iEwBxgCr/d9kI4CVIjIL57eWkSHZRwC74lzUmOnonduIyAJgHjBHg+PK+/Q7H0R/fa92RCQVJ3j8SVVf8J/eIyJDVbXc3wy7t/dKGHMnAeeKyDeBDGAATo1koIik+Gsh/erv25qwkoSqrlXVQao6WlVH4/ygmaGqu4ElwBX+0VjHA9VtzQB9nYjMBW4FzlXVhpBLS4BLRCRdRMbgDCD4pDfKGGPLgQn+kTlpOAMFlvRymWLO3/b/JLBeVX8ZcmkJsMCfXgC8nOiyxYuq3q6qI/zfv5cAb6vqpcA7wIX+bP3qna0G0jcsBb6J05HcAFzVu8WJqUeAdOBNf83rI1X9gaquE5FngS9wmrZuUFVvL5YzJlTVIyI3AssAN/CUqq7r5WLFw0nA5cBaEVnlP3cHcC/wrIhcjTPS8KJeKl8i3QosEpF/BT7DCaz9gs1EN8YY0y3WhGWMMaZbLIAYY4zpFgsgxhhjusUCiDHGmG6xAGKMMaZbLIAYY4zpFgsgxiSAiFzjX6L/tYPkedWf5/pEls2Y7rIAYkwCqOpvcWZhzxWRGyKvi8h1OJNFX1PVXye6fMZ0h00kNCZBRGQQ8DmQjbNMzQb/+Yk4M5QbcfZG2d17pTSm86wGYkyCqOpe4P8BWcAfRSRFRFKAP/rPXWvBw/QlthaWMQmkqi+LyFM4e5/c7T99HPC/ISvWGtMnWBOWMQkmIrnAaqDEf6oUmOrfuc+YPsOasIxJMH+guAdnNV43cJ0FD9MXWQAxJsFEJBNnie82h8OS5qYfsgBiTOLdDxwJ/ApYBXxfRL7Vu0UypuusD8SYBBKRM4HXcYbzHoez0+IKoApnCO/+XiyeMV1iNRBjEkRECoDfAa3AZararKqfA3cBg4H/6c3yGdNVFkCMSZzHgGHAT1V1Tcj5/wTeAy4Qkct6pWTGdIM1YRmTACJyOfB74F3gdFX1RVwfA6zB2f99iqqWJb6UxnSNBRBj4kxESnCCg+DM99jeQb5rgN8AbwJnqX1zmiRnAcQYY0y3WB+IMcaYbrEAYowxplssgBhjjOkWCyDGGGO6xQKIMcaYbrEAYowxplssgBhjjOkWCyDGGGO6xQKIMcaYbrEAYowxplv+P2LPIeNFYXwtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19f3b002c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y1,lw=3,label='scale=5')\n",
    "plt.plot(x,y2,lw=3,label='scale=3')\n",
    "plt.plot(x,y3,lw=3,label='scale=7')\n",
    "plt.xlabel('X',fontsize=20)\n",
    "plt.ylabel('PDF',fontsize=15)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>图5.7:不同规模参数下PDF的正态分布</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以使用相同的实例也可以获得CDF。`cdf`方法在给定的输入处给出了CDF，这可以是一个标量或一个数组。CDF如图5.8所示。CDF也显示了尺度参数的影响，但是PDF提供了一个更好的内部。因此，绘制PDF来查看分布或经验数据的行为总是更好的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x19f3b450d30>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19f3b3ae0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1 = rv1.cdf(x)\n",
    "y2 = rv2.cdf(x)\n",
    "y3 = rv3.cdf(x)\n",
    "# 绘制pdf\n",
    "plt.clf()\n",
    "plt.plot(x, y1, lw=3, label='scale=5')\n",
    "plt.plot(x, y2, lw=3, label='scale=3')\n",
    "plt.plot(x, y3, lw=3, label='scale=7')\n",
    "plt.xlabel('X', fontsize=20)\n",
    "plt.ylabel('PDF', fontsize=15) \n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>图5.8:不同规模参数下PDF的正态分布</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在水文学中还有其他相当常用的分布，例如柯西分布、卡方分布、指数分布和均匀分布等。让我们一起玩吧。首先，我们将生成这些分布的实例。除了位置和规模参数外，卡方分布还需要自由度参数。在均匀分布情况下，位置参数被定义为较低的范围，尺度参数定义为较高的范围，这在数学上是不正确的，而定义只是为了使函数更易于输入。图5.9显示了这些分布的PDF。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19f3af9dc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rv1 = st.cauchy(loc=0, scale=5)\n",
    "rv2 = st.chi(2, loc=0, scale=8)\n",
    "rv3 = st.expon(loc=0, scale=7)\n",
    "rv4 = st.uniform(loc=0, scale=20)\n",
    "\n",
    "# compute pdf\n",
    "y1 = rv1.pdf(x)\n",
    "y2 = rv2.pdf(x)\n",
    "y3 = rv3.pdf(x)\n",
    "y4 = rv4.pdf(x)\n",
    "\n",
    "# plot the pdf\n",
    "plt.plot(x, y1, lw=3, label='Cauchy')\n",
    "plt.plot(x, y2, lw=3, label='Chi')\n",
    "plt.plot(x, y3, lw=3, label='Exponential')\n",
    "plt.plot(x, y4, lw=3, label='Uniform')\n",
    "plt.xlabel('X', fontsize=20)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们从一些分布中生成了大量的随机变量来表示分布。为了探索样本的数量对经验分布的影响，我们将从同样的分布中产生随机数，但是使用不同的样本数，来检验它是如何影响经验分布的。我们将不使用任何定量的方法检验这个，因为直到这个阶段我们都没有谈论它们，我们只是用图形来表示。首先我们将用分布中最常使用的正态分布。我们将使用`matplotlib.pyplot`库中的`hist`函数计算PDF。我们为`hist`函数指定`normed=1`，这意味着直方图的面积应该等于1，而恰好是PDF。我们也使用`plt.axis`指定图形的范围，我们保持一致，这样我们可以比较容易的比较图形。`plt.axis`的参数是$[x_{min},x_{max},y_{min},y_{max}]$。图5.10显示了样本容量为100、1000、10000和100000的经验和理论的PDF。从图中可以看出，随着样本的增加，经验分布逐渐趋近于理论值。在样本容量为100时，数据的分布得非常糟糕，然而其他的情况下则相对较好。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19f3b4d5d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as st\n",
    "\n",
    "#正态分布\n",
    "rv = st.norm(loc=0,scale=5)\n",
    "\n",
    "x1 = np.linspace(-20, 20, 1000)\n",
    "y1 = rv.pdf(x1)\n",
    "\n",
    "# compute and plot pdf\n",
    "fig = plt.figure()\n",
    "fig.subplots_adjust(wspace=0.4)\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "x = rv.rvs(size=100)\n",
    "n, bins, patches = plt.hist(x, 20, normed=1, facecolor='yellow', alpha=0.5)\n",
    "plt.plot(x1, y1, 'r', lw=3)\n",
    "plt.xlabel('X', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.axis([-20, 20, 0, 0.10])\n",
    "plt.text(-18,0.08,'n=100')\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "x = rv.rvs(size=1000)\n",
    "n, bins, patches = plt.hist(x, 20, normed=1, facecolor='green', alpha=0.5)\n",
    "plt.plot(x1, y1, 'r', lw=3)\n",
    "plt.xlabel('X', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.axis([-20, 20, 0, 0.10])\n",
    "plt.text(-18,0.08,'n=1000')\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "x = rv.rvs(size=10000)\n",
    "n, bins, patches = plt.hist(x, 20, normed=1, facecolor='black', alpha=0.5)\n",
    "plt.plot(x1, y1, 'r', lw=3)\n",
    "plt.xlabel('X', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.axis([-20, 20, 0, 0.10])\n",
    "plt.text(-18,0.08,'n=10000')\n",
    "\n",
    "plt.subplot(2,2,4)\n",
    "x = rv.rvs(size=100000)\n",
    "n, bins, patches = plt.hist(x, 20, normed=1, facecolor='magenta', alpha=0.5)\n",
    "plt.plot(x1, y1, 'r', lw=3)\n",
    "plt.xlabel('X', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.axis([-20, 20, 0, 0.10])\n",
    "plt.text(-18,0.08,'n=10000')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>图5.10:样本数(n)对经验PDF和理论PDF的影响</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们也可以看到样本数量对经验分布的影响除了正态分布之外，还可以看到拉普拉斯分布。在本例中，我们分别使用`plt.xlim`和`plt.ylim`控制坐标轴的极限。在y轴情况下我们只定义`ymax`来控制坐标轴的最大极限，而对于x轴我们同时定义了两个极限。`axis`的极限可以用上一个例子中的坐标轴来确定，这个例子只是为了说明我们只能控制一个极限，而另一个极限是`plt`。图5.11显示了不同样本数的经验和理论pdf。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19f3b598f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+pqolIvJTEbnMq/Yw0F1ESoHvAKFlmDfhxHqbiCz3Xo2NY7dO/JOVsfRYJvoenJdsd8szjWiYFtKNGCfuQ1S3za67MfIf/0iAUZlPLKvChBPHfhuq2yCqOgeYE1H2Y1+6Argyyvt+BvwsRjtaLx9/XHv8Kh3a1I0HVh/dOrjzWVbuhGqF+fPhoosSa2d6YlpIN95+O5yOwbEAMHkyvOd1BN95B664It5WZTyx7mOZKyKNnQRlAS1TgbfeCqfPHQDtYtwAfv5A51jAickcS32YFtKFPXtg5UqXbtMGzj03tvedfz78/Ocu/c47ibEtw4lFALcn3Aojfrz5Zjh9waDY33f+QLjf223sf8oz/JgW0gn/3/GZZ8JJUcIaRePss50jqqqCVaucg+rRo/H3GbU06lhU9XYR6YBbtz8I2IHbXWzhcFMN1bo9lgsGx/7eSQPD6UWL4MgR6NgxfrZlAKaF9KH47WIu+cvLjPfy/xiSzZtvF8f25txcN88Smvh/9124/PJEmJmxxLJBcghud+/fgHuAJ4B1ImJjJanGpk2w1dtzd1K7hkO5RNIzN3x08fHj4TFmoxbTQnoxePmW2vSWsU14yAI3HBbC/7BmxEQsq8J+CdTgNn51xJ35vQz4YwLtMpqDXwDnDYC2TQywe+GgcHru3LiYlGGYFtKEk/YdpudHewCobpPF1pH9G3lHBBf64nqaFppMLI5lIvAjVX1PVStUdQ1up+8AEWnCI7GRcOb4FhhNaeITGsDFQ8PpV15puT2Zh2khTShcuKE2vXVkf463b9u0G0yaFB4KXr8eNtoe1KYQi2PJAzZFlG3ELaeMYS2rEQjHjsFrr4Xzl57S9HtMHgQ5Xi9n9Wq3a9nwY1pIE05ZEHYs688a2kDNemjfHi64IJy3B60mEet5LLGu3TeSxT/+Ed7YOGQInBoZqzAGOrZ1ziWEiSkapoVUp7KSgsXhHsb6ic14yAK4+OJw2rTQJFq6j+WNyHJVtR3AgVMML78azl7ao/6DvRrjkqEw1xPlnHvhK6EDw4pbYF9GYVpIdd59l5wjLj7o/ryT2TOgaUuFi73VY1277uebXtnxN+Zx99wfUpXTluLJxfGzNUOxfSyZgCq8tD6c/0wzn9DAOZZvek7qtU3ueOOT2rXMvszBtJAOvPRSbXL9WUOb/ZC1v29Xdg/oQc+P99D2WBUFizay7tyGg1gajpj2sQRhiNECVuyEjftdOret2+zYXAq7wahe8OEuqKiCl9fD1aPiY2eaY1pIA2pq4LnnarPrz2rBQxaw9txh9PzffwIw8p3V5lhiJPAz740E8PSH4fTMYZDTwogiV44Ip59ZXX89w0g1Fiyo3ct1pHMHNp/RjNWRPkomh7Vw6vx1tKlsLJqPAeZY0h9VeLoknL96ZMvv6XcsczbAp5X11zWMVOLpp2uTa84bRk2bJu7limBHYR/29e0KQM6RSgoW2bLjWDDHku4sXhw+TrhLDkwvaPk9h/eEkd4u/KNVMHtdy+9pGImmuhqeeaY2W3JBHIZwRer0Wka9+WEDlY0Q5ljSnb/8JZz+XByGwUJc4xPlI8vjc0/DSCRvvQXl5QB8enJHtowZFJfbfuhzUMPfXQP798flvplM4I5FRGaIyDoRKRWRW6NczxGRp73rC0VkkFfeXUTeEpHDIvK7oO1OSSoq4Iknwvl/Oy1+977u9PCJIq9vgi1b4ndvAzAtxJ2HHqpNrrpwFDXZ8fn3trOwD+VD3f7XNser4X//Ny73zWQCdSwikg08AFwMjACuFZEREdWuB/araiFwL3C3V14B3AZ8NyBzU5/nngs/PQ0+GS5s2URlHQZ0gYt8w2qPPhq/exumhXizezc8/3xtdulnxsX19ksvHhvOPPxwXO+diQTdYxkPlKrqJlWtBJ4CZkbUmQk85qWfBaaIiKjqp6r6T5yoDKjzhMaXz4CsZm6KrI/rfWJ69FF3PoURL0wL8eSxx1xUboCzzmLX4PjuTV01dTRVoaCuy5bB0qVxvX+mEbRj6Qds9eXLvLKodbxzwQ8AMccnEZEbRWSxiCzevXt3C81NYVauDJ9uly3w/8bEv43LToUeXiC+rVvrPBEaLSbhWoBWooeqKvj978P5G26IexMVnTqw+nxfh/K3v417G5lE0I4l2iN1ZOylWOrUi6o+qKpFqlrUs2fPJhmXVvzqV+H05cMhr1P828hpA1/xDSncc49b3mzEg4RrATJbD8VvF1P8djHP3HEtbN4MuL0rP88rTUh7Cy8fH848+SSUlSWknUwgaMdSBvgPRsgHttdXR0TaAF2AfYFYly5s3er+sEPccnbi2rppPLTzhgAWLYJ//jNxbbUuTAvxQJWzn55fm100s4jjHRITgmjbiHw+Om2Ay1RVwX33JaSdTCBox7IIGCoig0WkHXANMDuizmxglpe+AnhT1R6T6/CrX4XnOyZNgvGRIyhxpPdJcJ1vtdkvfpG4tloXpoU4MGTpZvqtc/64qm02H3xufCPvaBnzr/I9xP3P/8DevQltL10J1LF448Q3AXOBNcDfVLVERH4qIpd51R4GuotIKfAdoHYZpohsAX4DfFFEyqKsosl8PvrI/UGH+N73Et/mf54dDuT36qsuRL/RIkwLcUCVKX96oza7fMYYPu12UkKbXD/xFBg+3GUOHYK77kpoe+lKnHbTxY6qzgHmRJT92JeuAK6s572DEmpcOlBcDJVeiJWJE+GSS3APvwlkWA+47jq38gbg1lvhvfeaH5rfAEwLLWX4u2vptzbcW/nHv09KeJuaJXDHHXDFFa7g/vvhm9+E/PyEt51O2M77dGLJEnj88XD+rruC++d+++3Qzhu7fv/9OhFkDSNwKiqY+uDrtdmF/zKegz07B9J0cbeVbBvW12WOHWP59Z+pXUhgOMyxpAvV1fAf/+HCgoPrqUxK/BNaLQMHwte+Fs5/85tw4EBw7RuGnzvvpPs2t46hIjeHf157bnBti/D6DVNrs2PmrWDQ8i3BtZ8GmGNJF37/e9djAcjJgf/+7+Bt+MlPoHdvl96+HX44DXeypP9lGAlm3bo6cxuv3ziVo106BmrC5jMGU+Lb1/KZ37xkIfV9mGNJB1avhu9/P5z/4Q+hsDB4O04+ua5De2ARzLMw4kaAVFbCF75QO89YNrwfS+IcviVWXr1pBhW5OQD02LqXKQ+93sg7Wg/mWFKdigq49lo4etTlR44MZiVYfVx1lbdgwOPfn4cdh5Nnj9G6+K//qg2nUtU2m//7zmfchHoSONSjE6/fMKU2P/HZhfB//5cUW1INcyypjKoLT7Fypcu3bw9PPeWGwpKFCDzySHhIbNencNUzcMyGAYwE89RT8Otf12Zfv3EqOwv7JNEgWHxZEevO9h1/PGuWG6pr5ZhjSWXuuKPueSu/+Q2MSoHz53v3dnaFHhTf/Ri+NNvCvRiJY/58+OIXw/lLLmHB5yckzZxaRHjhezM5EFqRtn+/69Hv2pVcu5KMOZZU5de/dpPlIW64Ab7yleTZE8nUqXB3eGUM/7sKvvFKeNWaYcSLDz5w/6yPHXP5YcPgr39NmX1UR7t05Ok7rqayfVtXsGkTzJgBe/Yk17AkYo4l1VB1K16+6ztqY8oUeOCBlBFSLd89u26QygcWuSXRFl7fiAPFbxfz8P1fouLCSbVL2z/t0pH//tE0ipenVnTh7af25dnbPg9Z3r/UZcvgggtgx47kGpYkzLGkEseOwfXXww9+EC47bwC8MB7a/pyUW84rAvdfUvcY4z/9CS691I5vNVrM6a8uZ9Z/Pk77T11P5UjnDjz+q39nf79uSbYsOuvPPtUdAhZ6APzwQzjzTFi8OLmGJQFzLKnC2rVw7rl1T2o8/3yY869wUmKitcaFNlnwl8th1unhsnnzoKjIhX0xjKZy+DD8x39w+d0vuqOAcT2Vx359XdIn6xvli190x4WHei5lZXDeefC737WqYWJzLMmmosINfY0dW/fJZtYsmDs3tZ1KiOwseGQm3OaLBLBpkxPUt78Nn3ySPNuM9EHVLdc9/XR48MHa4p2De/HQH76c+k4lxL/+K8yZ4/Z9gdP4N74BF14Ia9Yk17aACDwIpeFx/LhbPvnjH8OWLeHydu2co/nWt+qZUykOyMAmkiXw0wvg9JvhS1+CgwfdP4rf/hYe/yP86Dy4cRzkhhxlcTKtNVKEUHyt/JKtXPDo2xQs2VTnesn5I3jxe5dR2TGJS+ybw/TpbtHBv/yLGxIDd+LrqFFOH7fdBgMGJNfGBGKOJWi2b3dLde+//8QT6E47zXWjTzst+nvTgc9/HsaPhy9/2Q2JAew7Ct+ZB3f8A244wzmYguSaaaQAR44w6s0PGf/3DxhQsrXOpYrcHF7+5iWsmjo69RatNEBkIMrsX89k8mMnc85T75FVo2447E9/ouaRh1lz3nA+uHw8H48egGYJxZOLo94zHTHHEgQbN7p/sn//O7zxxon7Pbp3d9GDb7wR2rZNjo3xpH9/d27LU0+58DPesbHsr4BfznevMxfA1Ve7J7uRI9Pqn4fRAvbtgzffhJdegr//nSsOHapzuSZLWPKZcbz1/yZz5OTcJBkZP6rbteGNG6ZQcsFIpv3Pa7U9sqwaZeQ7qxn5zmoO9OxMyQUjgcnuKIxkboCOE5LJB9IVFRXp4qBXZHz6KSxf7gJGLlkC774b/scaSe/ecNNN7hUajz2B4kRZ2kSKm1d27Bg8dDncuwA21bNSrHdvmDzZTfifcYabb+ratSXGNgsRWaKqRYE3HBCB66Gqyi1KWbrUaeH9993PKJPY1W2yWDn1NN675mz2DOwZnI0BM2TxRs793/cYsqye/wkdOrhFPBMmhLUwcGDgD14t1ULgjkVEZgD/DWQDf1LVuyKu5wCPA+OAvcDVqrrFu/YD4HqgGrhZVec21FbzhVQcvfjTShfCpPY1FcrLXY9k40YoLXX5hhDggsHw76e5ZbrtW0mnsboGXloPDy11gSuPN7JCpncuDOkKBZNhyBDo1w969XJOKPQzNzeuggvasQSpBYizYzl+HHbvdjvMQ68dO9xDVEgPW7Y0uqdpT//urJoymiWfOYPD3TvFx7Y0oPfGnZz54iJGvLOajgePNlj3WId27O/blT6nnQ0FBW5uxq+DXr3cg1hW/NZipZVjEZFsYD0wDSjDHX14raqu9tX5GnCaqn5FRK4BLlfVq72jV58ExgN9gdeBU1S1ur72igYO1MXf+Y4Tgf9VVXViWej16adweCUcrqz7OlQJlfU21TC5bZ0zmTYE/mU45AdzIFHKsv8oPH8qvPKKGxbZt69598nOhk6dTnzl5rrhhHbt3CuU9v9s29a9P/Rq0wb5+tcDcyxBawGgaMAAXfytb9X/tx+pjaNH3dLfw4fdMbyh9OHDcORIsz53TZaw/dS+bCwawrqzT2X7qX1b9TBoVlU1Q5Zu5tT31jJk6Wa6lzVTCyLu7z6aHiL//qNpIlILN92UVo5lIlCsqtO9/A8AVPVOX525Xp33RaQNsAPoiXfed6iuv1597RWJaOBbk7Kz4dRTYdw49yoqgjNfhXbZQVuS4hS7HzU1buhw4UJY9idYWg6rdjXfibcAgSAdS6BagOTo4WCPTpSfksf2U/IoP6UvH4/qT0WnDgFbkT502XmAAas+pk9pOXnrd5C3oZwOhysCt6OlWgh6HKYf4F/+UQZERpKrraOqVSJyAOjulS+IeG+/yAZE5EbgRi97TODD+JgeI9XV7vyU1avdCq8wPYBUCR6UArbcHkqkgC21nBpgWwnXAqSAHvYccq/56yOvpMrvPVXsgNSypUVaCNqxROvzRnaZ6qsTy3tR1QeBBwFEZHGqTMaaLdFJNVuCbC5KWVy1AKaHdLEDUs+Wlrw/6J33ZUB/Xz4f2F5fHa/73wXYF+N7DSNdMC0YGUvQjmURMFREBotIO+AaYHZEndnALC99BfCmuomg2cA1IpIjIoOBocAHAdltGPHGtGBkLIEOhXnjxDcBc3FLLB9R1RIR+SmwWFVnAw8DT4hIKe7p7BrvvSUi8jdgNVAFfL2xVTB4QwApgtkSnVZpSxK0AK30u26EVLEDMsiWjN4gaRiGYQSPRTc2DMMw4oo5FsMwDCOuZIxjEZED94e8AAAgAElEQVQrRaRERGpEpCji2g9EpFRE1onIdF/5DK+sVERuTZBdxSKyTUSWe69LGrMrkQTxmRtoe4uIrPK+h8VeWTcReU1ENng/ExYkTEQeEZFdIvKhryxq++K4z/ueVorIGYmyK96YFmK2J2la8NpPmh4SrgVVzYgXMBy3qedtoMhXPgJYAeQAg4GNuMnSbC89BGjn1RmRALuKge9GKY9qV4K/o0A+cwPtbwF6RJT9ErjVS98K3J3A9icBZwAfNtY+cAnwCm7PyFnAwqC+pzh8TtNC47YkVQueDUnTQ6K1kDE9FlVdo6rrolyaCTylqsdUdTNQiouxNB4oVdVNqloJPOXVDYr67Eokyf7M0ZgJPOalHwM+l6iGVPUfuNVVsbQ/E3hcHQuAk0UkL1G2xRPTQkwk+zPXRyB6SLQWMsaxNEC00Bn9GihPBDd5XchHfF3bINsPkYw2/SgwT0SWiAs1AtBbVcsBvJ+9ArSnofaT/V0lAtNCmFT4/aaaHuKmhbSK2S4irwPRDr7+oaq+WN/bopQp0Z1qs9ZeN2QX8AfgDu/edwC/Br7UgF2JJBlt+jlHVbeLSC/gNRFZG2DbTSXZ31WDmBZaTCr8ftNFD03+rtLKsajq1Ga8raHwF3EJixGrXSLyEPBSDHYliqSGAlHV7d7PXSLyPG44YqeI5Klqude93hWUPR71tZ/SYVNMCy0m6b/fFNRD3LTQGobC6gt/EUtIjRYTMRZ5OeHosskIyxHIZ46GiOSKSKdQGrgI9134w5bMAup72k4U9bU/G7jOWxFzFnAgNEyQxpgWwiRNC5CyeoifFoJcBZHIF+4PtQw4BuwE5vqu/RC3AmQdcLGv/BLcYUsbcUMIibDrCWAVsNL7BeU1ZleCv6eEf+Z62h2CW3mzAigJtY0LA/8GsMH72S2BNjwJlAPHvb+V6+trH9f9f8D7nlbhW12V6i/TQsz2JEULXttJ1UOitWAhXQzDMIy4EvhQWGObkrzu8NPe9YUiMiji+gAROSwi3w3KZsNIBKYFI1MJ1LGIO+f7AeBi3Kaoa8Wd3+3nemC/qhYC9wJ3R1y/F7dZxzDSFtOCkckE3WOJZVOSf5POs8AUEREAEfkcsAk3JmkY6YxpwchY0ubMexE5CnwfmAbU2/UX3xnfubm544YNGxY/642MZsmSJXtUtWdAzSVcC2B6MJpHS7WQTmfe3w7cq6qHvYe2qKjvjO+ioiJdvDjIY8yNdEZEPgqyuShlcdUCmB6M5tFSLQTtWJpyzneZ1D3newJwhYj8EjgZqBGRClX9XeLNNoy4Y1owMpagHUvtpiRgG25T0hci6oQ26bxP3XO+zwtVEJFi4LAJyUhjTAtGxpI2Z94bRiZhWjAymiB3mwb9GjdunAbNnj17dPLkyZqbm6tf//rX61xbvHixjho1SgsKCvQb3/iG1tTUqKrq3r17derUqVpYWKhTp07Vffv2qapqTU2NfuMb39CCggIdPXq0LlmypPZef/7zn7WwsFALCwv1z3/+c3AfMIPB/UNP+t9tol5B6yHZWqivDaNxWqqFpP+xJ/KVDMdy+PBhfffdd/UPf/jDCWI688wzdf78+VpTU6MzZszQOXPmqKrqLbfconfeeaeqqt555536ve99T1VVX375ZZ0xY4bW1NTo+++/r+PHj1dVJ77Bgwfr3r17dd++fTp48OBaARrNxxxLfEm2Fuprw2iclmqhNQShbBZbtmxh+PDh3HDDDYwcOZKLLrqIo0ePNvq+3Nxczj33XNq3b1+nvLy8nIMHDzJx4kREhOuuu44XXngBgBdffJFZs1zst1mzZtUpv+666xARzjrrLD755BPKy8uZO3cu06ZNo1u3bnTt2pVp06bx6quvxvkbMAxHOmqhoTaMxJNWYfODZsOGDTz55JM89NBDXHXVVTz33HOUl5fz17/+9YS6kyZN4r777qv3Xtu2bSM/P782n5+fz7Zt2wDYuXMneXku8GteXh67du2qfU///v1PeE995YaRKNJNCw21YSQecywNMHjwYMaMGQPAuHHj2LJlCz/60Y+45ZZbmnwv17usSwx7EKK+pzn3MoyWkG5aMI0kFxsKa4CcnJzadHZ2NlVVVdxzzz2MGTPmhNfNN9/c4L3y8/MpKyurzZeVldG3b18AevfuTXm5O96gvLycXr161b5n69atJ7ynvnLDSBTppoWG2jASjzmWJnLLLbewfPnyE14Ndf3Bdes7derEggULUFUef/xxZs50oaEuu+wyHnvMhYR67LHH6pQ//vjjqCoLFiygS5cu5OXlMX36dObNm8f+/fvZv38/8+bNY/r06Yn94IYRQSproaE2jABoycx/qr9asgpm8+bNOnLkyNr8Pffcoz/5yU9ieu/AgQO1a9eumpubq/369dOSkhJVVV20aJGOHDlShwwZol//+tdrlz/u2bNHL7zwQi0sLNQLL7xQ9+7dq6puieXXvvY1HTJkiI4aNUoXLVpU28bDDz+sBQUFWlBQoI888kizP6cRBlsVFpV01UJ9bRiN01ItZPRBXxYbyWgKIrJEVYuSbUeiMD0YsdJSLdhQmGEYhhFXzLG0JlTh2Wfh0Ufh2LFkW2MYyWXpUrj3XrBlyHHHlhu3Jp5/Hq680qV37oRbTzgN1zBaB3v3wvnnw+HD7mHrvfeSbVFGYT2W1sRvfxtO33Zb8uwwjGTzwQfOqQDMnw8xRBIwYsccS2vCt96fqqrk2WEYyeajiHOsNm9Ojh0ZijmW1kRNTd388ePJscMwks3GjXXzpaXJsSNDMcfSWqiuBm9Hcy2RT22G0VqIdCSRjsZoEeZYWgtbt57YQzExGa0VcywJJXDHIiIzRGSdiJSKyAnLkkQkR0Se9q4vFJFBXvl4EVnuvVaIyOVB257WROvqm5iSimkhSdTUnPi3b1qIK4E6FhHJBh4ALgZGANeKyIiIatcD+1W1ELgXuNsr/xAoUtUxwAzgjyJiy6VjJZpjsXHlpGFaSCLl5SeuAjMtxJWgeyzjgVJV3aSqlcBTQGRkuJnAY176WWCKiIiqHlHV0FKm9kDmxqJJBBs2nFhmT2nJxLSQLKJpYcsWWykZR4J2LP0A35pXyryyqHU88RwAugOIyAQRKQFWAV/xiasWEblRRBaLyOLdu3cn4COkKTYUlmokXAtePdNDJNG0UFVVdzm+0SKCdizRTtqJfNqqt46qLlTVkcCZwA9EpP0JFVUfVNUiVS3q2bNniw3OGKKJadMmF+bFSAYJ14JXz/QQSX3DXvagFTeCdixlQH9fPh/YXl8db9y4C7DPX0FV1wCfAqMSZmkmETlZmeX92o8ehe2RX78REKaFZOF3LFlZ0cuNFhG0Y1kEDBWRwSLSDrgGmB1RZzYwy0tfAbypquq9pw2AiAwETgW2BGN2mrNtWzjoZI8eUOSLhr1+fXJsMkwLycLvQC6+OJw2LcSNQB2LNw58EzAXWAP8TVVLROSnInKZV+1hoLuIlALfAULLMM8FVojIcuB54GuquidI+9MWv5CGDoVhw8L5NWuCt8cwLSQL1bp6+Oxnw2nTQtwIfImiqs4B5kSU/diXrgCujPK+J4AnEm5gJrJ2bTg9dCgMHx79mhEopoUksG0bfPqpS3ftCueeG75mWogbtvO+NbB6dTg9YkRdx2JPaUZrIlILhYWQne3yH30ER44kx64MwxxLayBSTDYUZrRWfuPTwtERcGcOdBni8qrw7XXJsSvDMMfSGoh0LAUF0Laty2/bBgcPJscuwwia3T4t9PQCHfT09eD32INWPDDHkuns2wc7drh0Tg4MGgRt2ri5lhA2tmy0FqI5lh4+x7LbHEs8MMeS6fiHuoYNC48n2wS+0dpQbdyx7DUtxANzLJlO5DBYCJvAN1obO3dCxX6XbtcJOnkRdHpajyXeWETUTCfCsRQXFwMwuqSEz3vFa59/nqdycmqvGUZGsjqityJexJzup4bL96535xaF5iCNZmE9lkzH3xvx9Vh29epVm+69c2eQFhlGcvBroaev996+C3T2ouvUHId1tjKspTTqWETkbBHJDcIYIwGsWhVO+4a/9vTsSbUXJ6nrJ5+QU1ERtGVph2khzfFrwT+vAtDn9HB6xYpg7MlgYumxvAuMDGVEJEtE/iEiQxt4j5FEiouLKS4u5p5bbqkNMnm8TRtuf/LJ2jrV2dns9kW7tV5LTJgW0pnly8PpPmPqXuvty5tjaTGxOJbI0N2Ci1XUKf7mGPGkT2iZMbCzd280q+6ve0efPuG65lhiwbSQrlRXw8qV4by/hxKZN8fSYmyOJYPxOxa/Ewmxs3fv2nRvX13DyDjWrw8fR9ypL+T2qnu9tzmWeGKOJYNpzLHs8DkW67EYGc2yZeF0n7EnXu9WAG296bOdO8Obio1mEety48+LSOgQjyzcKXZXishZEfVUVf8QN+uMFuF3LOXReiy+sl67drnjWdvYCvRGMC2kIw3NrwBIFvQeDWULXH7FCoiiGSM2Yv0vckuUsu9HKVPAxJQCtK2spMced0RHjQi7fL2TEEc6duRgp050PnSItlVVsGFD3Y2TRjRMC+lIHccSpccCbgLf71imT0+8XRlKo0NhqprVhFd2Y/cTkRkisk5ESkXk1ijXc0Tkae/6QhEZ5JVPE5ElIrLK+3lhcz5wa6H3rl21M817u3fneD0bvuoMkS1enHjD0hjTQpqiGjEUFqXHElluWmgRgc6xiEg28ABwMTACuFZERkRUux7Yr6qFwL3A3V75HuCzqjoad1yrHXTUAHm+s+yjza+E2NavXzizcGEiTTJ8mBYCZOtW8Hrv5HSGroOj1+s3Ppw2LbSImAfURUSAacBZQGhcZSfwPvC6qmoMtxkPlKrqJu+eTwEzAV+sBWYCxV76WeB3IiKq6nvkoARoLyI5qnos1s/Qmsjftq02XeZ3HhHUufbBB4k0KWMwLaQZCxaE033PdPMp0eg9Gtp0gKqj8PHHbgLf5lmaRUyORUTGAk8DBUA17olJgO7ePdaLyDWqurz+uwDQD9jqy5cBE+qro6pVInLAa8d/pvfngWXRhCQiNwI3AgwYMCCWj5eR5JeV1abL8vPrrbfd71iWL4eKCmjfPpGmpTXppAXPXtOD37HkR66x8JHVBvqOg4//6fIffACXXZZY2zKUWEK69AbmAkeBS4CTVLWvqubhNoZdClQCc0WkV/13creLUhb5dNdgHREZiRsS+I9oDajqg6papKpFPX07y1sTHY8cofu+fQBUZWc3OBR2tEMH9nbr5jLHj9ed5DTqkG5aANMDELtjAehrw2HxIJY5lm/ghHSeqs5V1crQBVU9pqqvAJO8Ojc1cq8yoL8vnw9sr6+OiLQBugD7vHw+8DxwnapujMH2Vkk/X2+lPC+P6kaWENfp0ZiYGsK0kG4cOwZLl4bz/SI7hRHk+66bFppNLI7lIuD3qlrv+bWq+gluaeWMRu61CBgqIoNFpB1wDTA7os5s3IQkwBXAm6qqInIy8DLwA1V9Lwa7Wy11hsEamF8JYRP4MWNaSDdWrHDOBdyR3LmN9Nr8jmfRIqipSZxtGUwsjqUQWNpoLVji1a0XVa3CPcnNBdYAf1PVEhH5qYiEBjMfBrqLSCnwHSC0DPMm7/63ichy79XYcEOrpH+M8yu1dfyOZf78RJiUKZgW0o333w+nJ05svH6XARDa83XwIJSUJMauDCeWyfsuwIEY6h0COjdWSVXnAHMiyn7sS1cAV0Z538+An8VgR+vm+HH6+VaEbYvBsezo04fKtm1pd/w4fPQRbNkCgwYlzsb0xbSQbrzn69BNmFB32UM0ROC88+DZZ13+7bdh9OhEWZexxBrdOJblk6G6RjJZsoScSjf0f6BzZz7p0qXRt9RkZ/Oxf8XQO+8kyrp0x7SQTqg6xxBi0qTY3jd5cjhtWmgWse5jmSsiVXG6l5FI3nqrNrl58ODw8auNsGXgQAo3enPA77wDs2Y1/IbWi2khXSgpgd27Xbp7dxg1Cv4ew/vOPz+cfucd56Bi1JHhiEUAtyfcCiN++BzLliYMZ33kr+t/yjP8mBbSCZ8WmDwZsmIMNDJihHNEe/e6HfurV8PIkY2/z6ilUceiqreLSAfcuv1BwA7c7mKLs55qVFbWGVPe3ATHsr1vX+jQwZ1ZsXmzC4PRv3/jb2xFmBbSDL9jueCC2N+XleWGzZ5/3uXfecccSxOJZYPkEFzYiL8B9+DiEq0TkYsSbJvRVD74AI4cAWBf164cOPnkmN9anZ0N55wTLnjjjXhbl/aYFtKImpq68yNNcSxQd57FtNBkYukb/hKowW386og783sZ8McE2mU0h9deq002ZRislmnTwulXXmm5PZmHaSFdWLoUvOgT9OrV9OMg/Fp47TUXlcKImVgcy0TgR6r6nqpWqOoaXAiJASKSl1jzjCbx8su1yY0FBU1//8UXh9Pz5rmDvww/poVUptj3+m5YC/SZDrdLOJxnLAwbBgMHuvShQ3WXLRuNEotjyQM2RZRtxC2ntNCfqUJ5OSxZAkB1VlbzHMuoURDaLPnJJ3VjLBlgWkgfNvgcy9BLm/5+kboPWtaDbxKxnscS69p9I1nMCe+z+3jAACqaE6FYBC65JJw3MUXDtJDqHN4B2xe5tGRDYRNPgiz2Xp/4tPDnV+r2iIwGidWxzBWRXaEXUO6Vv+Ev964ZycA3DLZh6NDm38f/lPbSSy0wKGMxLaQ6G3wPRAPOhfaxL2Kpw+ALIbudS+9aBQc+brltrQTbx5IJHD1aZ+J+fUscy9SpkJPjAvetXAmlpVDYYNir1oRpIR1Y74vl2ZxhsBDtcmHQBbBxrsuvfg4mfrtltrUSYtrHEoQhRguYMwcOH3bpoUPZ06NH8+/VqRNMnw6zPXE+8wz84ActtzEDMC2kAccO1u2xnNrCg7pGXOFzLM+YY4mRQM+8NxLE00+H01df3fLwE1f64h4+80zL7mUYQbL2Raj2wuT3GQM9Tm3Z/YZ9zs3TAJS9Dwe2NlzfAMyxpD+HD9edC7n66pbf87OfhXbe2PKyZbDRzpEy0oQS30PWyDhooWMPN9cSYs1zLb9nK8AcS7rz0ktujgVc2IlRo1p+zy5d3HBYiL/8peX3NIxEc3Q/bJwXzo+8Kj73HeHrwa80LcSCRWFNU4qLiwH4t7/8pfZEqTd79uQfXnlL7gkwsl272oNAPrn3Xk6+7bbYg/gZRjJY9Veo8XbI9z0Tug6Jz31HfB5e+YYbYitfAjtWAKfH594ZSuD/KURkhoisE5FSEbk1yvUcEXnau75QRAZ55d1F5C0ROSwivwva7lTk5E8+ocAbplJgxenx+2NfO2wYRzp0cO0cOGDxkhKAaSGOqMLSh8L5Mf8vfvfu0A2GXx7OL3s4fvfOUAJ1LCKSDTwAXAyMAK4VkRER1a4H9qtqIXAvcLdXXgHcBnw3IHNTnrFLl9aeJlVaWNikoJONUd2mDSv9J+c9bGKKJ6aFOLNoEexc6dJtO8LoL8T3/mOvD6dX/gUqKuJ7/wwj6B7LeKBUVTepaiXwFDAzos5M4DEv/SwwRUREVT9V1X/iRNXqyaquZuzy5bX5pWecEfc2lvnv+fzzsNOiw8cR00I8+aMvDujIq6B94yenNonBF8LJg1y6Yr+tlmyEoB1LP8C/Xq/MK4taR1WrcGeMd4+1ARG5UUQWi8ji3aHT4zKQkSUldD50CIDDubmsO+WUuLexs3dvykKxwyor4Xc26hJHEq4FaCV62LkT/vrXcP6MG+LfhmTB2C+H87/+tRt+M6IStGOJtsEi8rcTS516UdUHVbVIVYt69uzZJOPSBlXOmT+/NvvB+PHUZGcnpKn5EyeGM7//PXz6aULaaYUkXAvQSvRw//0uUgRAv/GQP7Hh+s2l6CvQxs07smKFzTs2QNCOpQzwH0uYD2yvr46ItAG6APsCsS5deO01+njDUpVt27KoqChhTa0dPpz9obmbffvg0UcT1lYrw7QQDw4fdg88Ic6+JXHn03fsDmO/FM7fc09i2skAgnYsi4ChIjJYRNoB1wCzI+rMBmZ56SuAN1Wtz1mLKviWBS8bO5ajHTsmrLmarCze9/da7rorvG/GaAmmhXhw//2wf79Ldy2AYZc3XL+lnPVtNywG7swi38iBESZQx+KNE98EzAXWAH9T1RIR+amIhIL6PAx0F5FS4DtA7TJMEdkC/Ab4ooiURVlFk/n83//B++8DUJWdXXeoKkEsGzMGevd2mW3b4IEHEt5mpmNaiAP79sHdd4fz53wfshIzJFxLtwIYdU04f+utNtcSBcnkB6CioiJdvHhxss2IH1VVMHYsfPghAAsmTODVGTMCabq4Vy/4+tddpmtX2LQJ4ri8ORUQkSWqmrhxxSSTcXr4/vfhl7906VNOgatLICuAPd/7NsIfhoVPWH355brnGGUALdWCbaVOJ37/+1qnUtm2Le+ed15wbX/5yzDE28m8fz/8+MfBtW0YkaxdC/feG87fcUcwTgVcr+XGG8P5b387vHjAAMyxpA/btsGPflSbfffcc/k0Nze49tu1gzvvDOd/9zu3Kc0wgkYVvvpVOO6Fb5k4Ea64IlgbbrsNOnd26fXr3dyjUYs5lnRA1Q1DeftWGD6c+eecE6gJxcXFFJeUUFpQUGvTjs9+ljt8zs4wAuHhh+Htt106Oxv+53+Cj2PXpw/84hfh/C9+AatXB2tDCmOOJYUpLi6muLiYlz7zGXjxxdryP48fT3WC9q00iAgvXXopx9u4IYc+O3cy1dbyG0Gydi1885vh/Le+BaedlhxbvvIVGD/epSsr4ZprbMWkhzmWFKf3jh1MnxcOBb7wzDPZMmhQ0uz5pGtXXp8ypTY/ccECt1LNMBLNkSNw7bXuJ8Dw4fDTnybHlmLgjmwY9zC0ae/KVq2C877trhUnx6xUwRxLCnPSoUN84cknaeutPtnZqxevXXRRkq2ChRMm1A0h86//CitXJs8gI/P5SQ0UXQeh+HjZ7WDSk/DLjsn9R95rFEz/bTi/5I+w8P4kGZM6mGNJVQ4c4NqnnqLLwYMAHGvXjmevuIKqNilwhI4IL86cyYHQ5OWhQ3DppbDVjm01EoAqvPa9uqc3zvhv6JMiZ6KMu7HuaZVzvwVrX0iePSmAOZZU5MABmD6dfttdhI8aEZ658kp2p1CspyMdO/LXL3yBipwcV1BWBuefD1u2JNUuI8NQdftV3v91uGz8zS5uV6ogAjMfhfyzXF5r4Jmr4IXW61zMsaQaW7fC5MmwcGFt0cuXXkppYWH970kSu3r35m9XXQVt27qCzZth0iQ31mwYLeX4cTdB7o/JNexzMP03ybOpPtp2gGtedGFlwJ1kecUVrTa2njmWVGL+fDjzzPA4MvDSJZewZNy4JBrVMJuGDHFntYR6Llu3un0Fzz6bXMOM9GbXLrjoInjwwXDZsM/BFU8nPmxLc8ntBbPegm5DXb66Gr70JbeKLbTnppVgjiUVqKx0mx/POy98mFabNrx42WUsPvPM5NoWA8WLFvH4lVdyrF07V/Dpp3DllSwbO5a7bj3hxF3DaJgXX4RRo8J7VQBG/6tzKtntkmZWTHTpD198B3r5Tl+97z4466xW1ZM3x5JMVN1S3dGj4ec/h5oaV96tG7z2GsvGjk2ufU1gU0EBf7r+evZ261ZbNnb5cr72+9+74YDq6iRaZ6QF69bBZZfB5z4H/kPJfv5zuPyJ1HcqITrlwfXz4V/+JVy2dCmMGwe33BKOxpzBWBDKZFBTAy+95MaO//nPutfOPx/+/GcYNIhiX3j8dKH90aN85uWXGVVSUqd8V8+e/POccygZOZJq38q2VPqMFoQySXz4oTuR8S9/CQd2BOjbFx55BKZPT899IT+ucfHMfvjDurHETj7Zbez86lehV6/k2dcALdWCOZYg2bTJHaH6xBOwYUOdSxU5Obw1eTIfTJiAJuqgogAZvno1l86Zw0kRJ04ezs1l2ZgxlIwaxY7evSm+/fYkWXgi5lgC5MAB+PvfnRbeeuvE62O+CBf9Gjp0O/FaurFnLcy+HrZGnN2S3Q6uvcpt+pw61cXjSxHMsTRA0oV05Ig7O2XePPfyTcqHqM7KYukZZ/DW5MkcCTKoZAC0q6xk4vz5nDN/Pu2iTF7u6d6dHl/4ghPV+edDly5JsDKMOZYEUl3teiavveZe77wTPSLwwPOdQ+mbugtWmoUqrH4W3vwv2Fd64vVu3VzPbOpUmDIFBgxI3EmYMWCOpQECE9KxY26p7caNrieyfDksWQJr1tQ7t1CRk8OSceNYOGECB0MbDTOUjkeOMG7JEs5ctIjOoUCakYjA0KHuvJmxY124jiFD3CuBJ2TWNcEcS4upqXGRuEtLnR5WrXJaWL7cLeqIisDwy2Hif0L/sxNrX7KpPu42ei74LWxbWH+93r3DWhg9GgoK3Ktbt0AcTto5FhGZAfw3kA38SVXvirieAzwOjAP2Aler6hbv2g+A64Fq4GZVndtQWzELSdUtBzx+3P3xHz584uvQITfptmtX3df27W5zYAzfY3VWFhsLClh52mmsO/VUjof2f7QSsqqrGVpaysiSEoatXRu1FxOVvDzo18+NR/fq5UTXq5cbq+7Uyb06dw6nc3Pd8ud27dwrxsi3QTuWILUAMepB1T0MHT/uAir6//79ejhw4EQt7NwJH30U+9kkvU+H0/4NRl0LnfvF9p5MonwprHoSSp6GgzFGrejcGQYOrKuDXr2ge/foWujUqa4WYozckVaORUSygfXANKAMd+73taq62lfna8BpqvoVEbkGuFxVr/aOXn0SGA/0BV4HTlHVepcbFXXsqIsHDw47jdCrqqpuPkErlhTY06MHmwcPZmNBAVsGDeJYaL9HK6ft8eMM+PhjBm/axJDNm+mzYwdZifpbzM6uK66cHLepMzs7/GrTBlmxIjDHErQWAIo6dNDFAweeqIdIbSSKkyG8rGkAAAbaSURBVPJg4CQYMg0KpkGXAYlrK53QGtixHDa9AZvfgK3vQeXhxLSVlRXWQUgL7drVaiBeWgg68NR4oFRVNwGIyFPATMB/kMFMwmtAngV+JyLilT+lqseAzd454OOB9+tt7ejRQM5IqBHhYOfO7OvWjf1du7K7Z0+25+Wxo08fKs2RROV427ZsLChgo3e+S5vjx+m1axd5O3bQZ8cOuu7fT7d9++hy4ADZoWXYzaW62s13haLipgbBagGgosIt6U00HXu4HejdCqH7KZB3BuSNc8twjRORLO87OgPOucU5mn2lrkdTvgz2rYf9m9yRyMfrG06MkZoa93dQUREf2+shaMfSD/D3+cqACfXVUdUqETkAdPfKF0S894T+s4jcCITODT0m8GF8TG8AVTc0cOCAm2uJTg9gT8JtiQ2zJTqnBthWwrUASdLDkT3u1dAcQur83lPFDkgtW1qkhaAdS7RZp8jxj/rqxPJeVPVB4EEAEVmcKpOxZkt0Us2WIJuLUhZXLYDpIV3sgNSzpSXvD3rnfRnQ35fPB7bXV0dE2gBdgH0xvtcw0gXTgpGxBO1YFgFDRWSwiLQDrgFmR9SZDczy0lcAb6pbYTAbuEZEckRkMDAU+CAguw0j3pgWjIwl0KEwb5z4JmAubonlI6paIiI/BRar6mzgYeAJb0JyH05wePX+hpvcrAK+3tgqGLwhgBTBbIlOq7QlCVqAVvpdN0Kq2AEZZEtGb5A0DMMwgseiGxuGYRhxxRyLYRiGEVcyxrGIyJUiUiIiNSJSFHHtByJSKiLrRGS6r3yGV1YqIgk5kUpEikVkm4gs916XNGZXIgniMzfQ9hYRWeV9D4u9sm4i8pqIbPB+dk1g+4+IyC4R+dBXFrV9cdznfU8rReSMRNkVb0wLMduTNC147SdNDwnXgqpmxAsYjtvU8zZQ5CsfAawAcoDBwEbcZGm2lx4CtPPqjEiAXcXAd6OUR7Urwd9RIJ+5gfa3AD0iyn4J3OqlbwXuTmD7k4AzgA8bax+4BHgFt2fkLGBhUN9THD6naaFxW5KqBc+GpOkh0VrImB6Lqq5R1WjxKmrDX6jqZiAU/qI2pIaqVgKhkBpBUZ9diSTZnzkaM4HHvPRjwOcS1ZCq/gO3uiqW9mcCj6tjAXCyiKRFTBLTQkwk+zPXRyB6SLQWMsaxNEC00Bn9GihPBDd5XchHfF3bINsPkYw2/SgwT0SWiAs1AtBbVcsBvJ9BH6lXX/vJ/q4SgWkhTCr8flNND3HTQtAhXVqEiLwO9Ily6Yeq+mJ9b4tSpkR3qs1ae92QXcAfgDu8e98B/Br4UgN2JZJktOnnHFXdLiK9gNdEZG2AbTeVZH9XDWJaaDGp8PtNFz00+btKK8eiqlOb8baGwl/EJSxGrHaJyEPASzHYlSiSGgpEVbd7P3eJyPO44YidIpKnquVe93pXUPZ41Nd+SodNMS20mKT/flNQD3HTQmsYCqsv/EUsITVaTMRY5OWEo8smIyxHIJ85GiKSKyKdQmngItx34Q9bMguo72k7UdTX/mzgOm9FzFnAgdAwQRpjWgiTNC1AyuohfloIchVEIl+4P9Qy4BiwE5jru/ZD3AqQdcDFvvJLcIctbcQNISTCrieAVcBK7xeU15hdCf6eEv6Z62l3CG7lzQqgJNQ2Lgz8G8AG72e3BNrwJFAOHPf+Vq6vr31c9/8B73tahW91Vaq/TAsx25MULXhtJ1UPidaChXQxDMMw4kprGAozDMMwAsQci2EYhhFXzLEYhmEYccUci2EYhhFXzLEYhmEYccUcSytARN4UkRXizk33l39eRFREpiXLNsMIGtND4rHlxq0AERmG2ztwq6r+xis7CVgDzFfVq5Npn2EEiekh8ViPpRWgqmtxcZluF5FQ8LjbgS7At5NmmGEkAdND4rEeSytBRDoCq3GhMn4GLAG+p6r3JtUww0gCpofEYo6lFSEiM4EXcAcMHQTGqWpVUo0yjCRhekgc5lhaGd4RqOOAC1X1rWTbYxjJxPSQGGyOpRUh7vzzsbizFCYn1xrDSC6mh8RhPZZWgohkAQtxEW9fw51pPVJVNyXVMMNIAqaHxGKOpZUgIl8D7gPOwIUmLwHWqupnkmqYYSQB00NisaGwVoB39OnPgftVdaWqHgNuBi71JjANo9Vgekg81mNpBYjI48BUYJiqHvSVvwCcDoxQ1aPJss8wgsT0kHisx5LhiMgk4N+B//SLyOObQC/gvwI3zDCSgOkhGKzHYhiGYcQV67EYhmEYccUci2EYhhFXzLEYhmEYccUci2EYhhFXzLEYhmEYccUci2EYhhFXzLEYhmEYccUci2EYhhFX/j/9wJhqk9cjcAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19f3b598828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rv = st.laplace(loc=0, scale=15)\n",
    "x1 = np.linspace(-100, 100, 1000)\n",
    "y1 = rv.pdf(x1)\n",
    "\n",
    "# compute and plot pdf\n",
    "plt.clf()\n",
    "fig = plt.figure()\n",
    "fig.subplots_adjust(wspace=0.4)\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "x = rv.rvs(size=100)\n",
    "n, bins, patches = plt.hist(x, 20, normed=1, facecolor='yellow', alpha=0.5)\n",
    "plt.plot(x1, y1, 'r', lw=3, label='scale=5')\n",
    "plt.xlabel('X', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.ylim(ymax=0.04)\n",
    "plt.xlim((-100,100))\n",
    "plt.text(-80,0.035,'n=100')\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "x = rv.rvs(size=1000)\n",
    "n, bins, patches = plt.hist(x, 20, normed=1, facecolor='green', alpha=0.5)\n",
    "plt.plot(x1, y1, 'r', lw=3, label='scale=5')\n",
    "plt.xlabel('X', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.ylim(ymax=0.04)\n",
    "plt.xlim((-100,100))\n",
    "plt.text(-80,0.035,'n=1000')\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "x = rv.rvs(size=1000)\n",
    "n, bins, patches = plt.hist(x, 20, normed=1, facecolor='black', alpha=0.5)\n",
    "plt.plot(x1, y1, 'r', lw=3, label='scale=5')\n",
    "plt.xlabel('X', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.ylim(ymax=0.04)\n",
    "plt.xlim((-100,100))\n",
    "plt.text(-80,0.035,'n=10000')\n",
    "\n",
    "plt.subplot(2,2,4)\n",
    "x = rv.rvs(size=10000)\n",
    "n, bins, patches = plt.hist(x, 20, normed=1, facecolor='magenta', alpha=0.5)\n",
    "plt.plot(x1, y1, 'r', lw=3, label='scale=5')\n",
    "plt.xlabel('X', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.ylim(ymax=0.04)\n",
    "plt.xlim((-100,100))\n",
    "plt.text(-80,0.035,'n=100000')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>图5.11:拉普拉斯分布的样本数(n)对经验PDF和理论PDF的影响</center>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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